If there is one place in the country where the proposed Panama Canal treaties could be expected to be unpopular it is in this conservative region of New England.

The state's archconservative governor, Meldrim Thomson, Jr., has publicly denounced them. The state's dominant newspaper, the Manchester Union Leader, is a constant critic of the treaties. But yesterday in the gymnasium of Nashua High School, President Carter provoked a surprisingly strong surge of support for the treaties from 1,500 people, many of them high school students from throughout the state.

The president was more than halfway through a question-and-answer session with the students when the canal treaties issue arose. As he answered, a handful of protesters in the back of the building began to heckle him, at one point accusing him of lying to public about the treaties.

Carter ignored the heckling and finally said, "I think the Panama Canal treaties are good . . ."

With that, the gymnasium crowd erupted with a sustained standing ovation as the beaming president looked on.

"You've made my trip worthwhile," he said.

Nashua, which is near New Hampshire's border with Massachusetts, may be the state's most liberal city. Nonetheless, the strong pro-treaties reaction here was surprising, clearly pleasing the president and bolstering his hopes for Senate approval of the treaties.

Carter, dogged throughout the day by questions involving the coal strike negotiations, arrived here yesterday morning after an overnight stay in Bangor, Maine. It was his last stop on a two-day swing through three New England states that marked the beginning of what is expected to be a concerted presidential campaign effort this year for Democratic members of Congress.

In Rhode Island and Maine on Friday, Carter attended fund-raising events for Sens. Claiborne Pell (D-R.I.) and William D. Hathaway (D-Maine). Yesterday in Nashua he had praised for Sen. Thomas J. McIntyre (D-N.H.). All three are up for reelection this year.

Moreover, any trip to New Hampshire in February would have political overtones. It will be two years ago next Friday that Carter finished first in the New Hampshire primary, greatly boosting his march toward the Democratic nomination and, ultimately, the presidency. And two years from now in New Hampshire he could well face a challenge in the state's primary from California Gov. Edmund G. Brown Jr. and other dissatisfied Democrats.

When he arrived in the state yesterday morning, the president was greeted - as presidents before him have been greeted - with a denunciation on the front page of the Union Leader. "Will Mr. Carter Lie Again Today About the Canal?" read the headline over the front-page editorial by the paper's publisher, William Loeb. Inside, there was a column suggesting that Carter is the most incompetent president in the nation's history.

But if Loeb, and his ally Thomson are representative of political sentiment in New Hampshire, it was not evident inside the Nashua High School gym.

When Carter was asked about Thomson's recent trip to South Africa, during which the Republican governor expressed support for the racial policies of the South African government, the president replied:

"Well, he has a right to go to South Africa. There are very few things on which your governor and I agree."

That answer, like his call for approval of the Panama Canal treaties, provoked enthusiastic applause.

Answering questions from the students, Carter made a direct appeal for public understanding and patience over the pace of his administration's accomplishments. Asked about his campaign promises, he replied:

"When I made all those promises to the American voters, I never said that I would accomplish everything the first year. I have only been in the office 13 months and have about three more years to go. There has been impatience exhibited by the American electorate and also by the news media. But when you get to the end of the first 12 months and say you haven't done everything you promised in the four years, that is not a fair way to measure what I and the Congress have been able to do together.

". . . I think the American people have to realize the difficulty of some of these issues, be patient with me and the Congress recognize what we have accomplished . . ."

The statement was one of the president's most defensive comments about his record in office.

Carter opened the meeting with the students with a call for reform of the civil service system, saying he will propose his reorganization and reform plans to Congress next month.

"We need an improved civil service on the federal level, a system that rewards those who serve well, disciplines those who are inefficient or incompetent or irresponsible, and gets rid of those who can't do the jobs well at all," he said. "We must restore the merit system to the civil service."

For the second day in a row, in response to a question, the president also defended the administration's proposed Middle East arms sale, under which the United States, for the first time, would supply warplanes to Egypt as well as sophisticated F15 fighters to Saudi Arabia and Israel.

The shipment of the F15s to the Saudis and shorter-range F5Es t) Egypt. Carter said, "will not upset the balance of strength in the Middle East. I would say that the Israeli air force will still be the dominant and most effective air force there by far."

The president returned to Washington yesterday afternoon and went immediately to the White House for a meeting on the coal strike with Labor Secretary Ray Marshall. Carter will make his next political trip Monday night when he flies by helicopter to Wilmington to attend a fund-raising even for Sen. Joseph R. Biden Jr. (D-Del.).